What is the answer to (z+1)/(z-1)=2i ?

The answer to (z+1)/(z-1)=2i is z= 3/5-4/5 i

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(z+1)/(z-1)=2i

\frac{z + 1}{z - 1} = 2 i

z = \frac{3}{5} - \frac{4}{5} i

Solution steps

\frac{z + 1}{z - 1} = 2 i

Substitute

z = x + y i

\frac{x + y i + 1}{x + y i - 1} = 2 i

Multiply both sides by

x - 1 + i y

\frac{x + y i + 1}{x + y i - 1} (x - 1 + i y) = 2 i (x - 1 + i y)

Simplify

(x + 1) + i y = - 2 y + 2 i (x - 1)

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[x + 1 = - 2 y y = 2 x - 2]

[x + 1 = - 2 y y = 2 x - 2] : x = \frac{3}{5}, y = - \frac{4}{5}

Substitute back

z = x + y i

z = \frac{3}{5} - \frac{4}{5} i

\frac{( - 2 + 9 i )}{( - 6 + i ) ( s )} = - 1

(z - i)^{2} = 2

r (t) = t i + t^{2} j + 2 t k, (2, 4, 4)

x^{2} + x + 1 + i = 0

x + i (y + 1) = 2 x + i 2 y

What is the answer to (z+1)/(z-1)=2i ?
The answer to (z+1)/(z-1)=2i is z= 3/5-4/5 i